From her home, Glera traveled 5.8 miles north to the grocery stare, then 2.1 mlles west to the library. What is the distance thom her home to the library

6.16 miles

Step-by-step explanation:

When solving word problems like these, I like to start by drawing a picture.

So, Glera starts at her home and moves north by 5.8 miles. Then, she walks west by 2.1 miles to the library. The problem wants you to find the distance from her home to the library.

I've attached a drawing I made to help me visualize the problem. The distance from her home to the library is the hypotenuse of the triangle. To solve for it, you would use the equation + = .

a and b are the sides of the triangle, and c is the hypotenuse.

 + =

33.64 + 4.41 =

38.05 =

To find c, you would take the square root of 38.05, which is about 6.16 if you use a calculator.

So, the distance from her home to the library is 6.16 miles!

answer: 15

step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12